R version 3.0.2 (2013-09-25) -- "Frisbee Sailing"
Copyright (C) 2013 The R Foundation for Statistical Computing
Platform: i686-pc-linux-gnu (32-bit)

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> x <- c(679,687,638,628,604,713,712,693,697,555,486,470,465,426,384,379,381,380,351,346,339,336,333,324,324,321,304,343,407,389,361,353,361,387,692,704,742,721,843,847,945,946,946,945,1082,1075,820,832,851,1090,1203,1239,1535,1527,1480,1452,1383,1381,1429,1376,1602,1597,2003,1958,1997,1986,2129,2115,2297,2250,2309,2648,2627,2711,2732,2825,2932,2910,2969,2999,2965,2846,2847,2751)
> par3 = 'additive'
> par2 = 'Triple'
> par1 = '12'
> par3 <- 'additive'
> par2 <- 'Triple'
> par1 <- '12'
> #'GNU S' R Code compiled by R2WASP v. 1.2.327 ()
> #Author: root
> #To cite this work: Wessa P., (2013), Exponential Smoothing (v1.0.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_exponentialsmoothing.wasp/
> #Source of accompanying publication: 
> #
> par1 <- as.numeric(par1)
> if (par2 == 'Single') K <- 1
> if (par2 == 'Double') K <- 2
> if (par2 == 'Triple') K <- par1
> nx <- length(x)
> nxmK <- nx - K
> x <- ts(x, frequency = par1)
> if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
> if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
> if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
> fit
Holt-Winters exponential smoothing with trend and additive seasonal component.

Call:
HoltWinters(x = x, seasonal = par3)

Smoothing parameters:
 alpha: 0.9724484
 beta : 0.06518791
 gamma: 0.74673

Coefficients:
            [,1]
a   2802.5291589
b     33.6185308
s1   -29.5841938
s2   -33.0070251
s3   -38.0453315
s4   -32.6618396
s5    -6.1538864
s6    -6.9210563
s7    74.1214080
s8    82.4553638
s9   110.7401474
s10   -0.2860481
s11  -51.5380959
s12  -50.5346676
> myresid <- x - fit$fitted[,'xhat']
> postscript(file="/var/wessaorg/rcomp/tmp/1rycs1386860795.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,1))
> plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
> plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
> par(op)
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/2wf6t1386860795.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> p <- predict(fit, par1, prediction.interval=TRUE)
> np <- length(p[,1])
> plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/3lp8x1386860795.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow = c(2,2))
> acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
> spectrum(myresid,main='Residals Periodogram')
> cpgram(myresid,main='Residal Cumulative Periodogram')
> qqnorm(myresid,main='Residual Normal QQ Plot')
> qqline(myresid)
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'alpha',header=TRUE)
> a<-table.element(a,fit$alpha)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'beta',header=TRUE)
> a<-table.element(a,fit$beta)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'gamma',header=TRUE)
> a<-table.element(a,fit$gamma)
> a<-table.row.end(a)
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/4pc5m1386860795.tab") 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'t',header=TRUE)
> a<-table.element(a,'Observed',header=TRUE)
> a<-table.element(a,'Fitted',header=TRUE)
> a<-table.element(a,'Residuals',header=TRUE)
> a<-table.row.end(a)
> for (i in 1:nxmK) {
+ a<-table.row.start(a)
+ a<-table.element(a,i+K,header=TRUE)
+ a<-table.element(a,x[i+K])
+ a<-table.element(a,fit$fitted[i,'xhat'])
+ a<-table.element(a,myresid[i])
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/525p11386860795.tab") 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'t',header=TRUE)
> a<-table.element(a,'Forecast',header=TRUE)
> a<-table.element(a,'95% Lower Bound',header=TRUE)
> a<-table.element(a,'95% Upper Bound',header=TRUE)
> a<-table.row.end(a)
> for (i in 1:np) {
+ a<-table.row.start(a)
+ a<-table.element(a,nx+i,header=TRUE)
+ a<-table.element(a,p[i,'fit'])
+ a<-table.element(a,p[i,'lwr'])
+ a<-table.element(a,p[i,'upr'])
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/6v62n1386860795.tab") 
> 
> try(system("convert tmp/1rycs1386860795.ps tmp/1rycs1386860795.png",intern=TRUE))
character(0)
> try(system("convert tmp/2wf6t1386860795.ps tmp/2wf6t1386860795.png",intern=TRUE))
character(0)
> try(system("convert tmp/3lp8x1386860795.ps tmp/3lp8x1386860795.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.673   0.508   3.154